Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Evaluation of a MULTIFIT-based scheduling algorithm
Journal of Algorithms
Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
Bin packing with restricted piece sizes
Information Processing Letters
Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Tighter bound for MULTIFIT scheduling on uniform processors
Discrete Mathematics
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
Various notions of approximations: good, better, best, and more
Approximation algorithms for NP-hard problems
On the efficiency of polynomial time approximation schemes
Information Processing Letters
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Makespan Minimization in Job Shops: A Linear Time Approximation Scheme
SIAM Journal on Discrete Mathematics
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Carathéodory bounds for integer cones
Operations Research Letters
Parameterized Complexity and Approximation Algorithms
The Computer Journal
Improved approximations for hard optimization problems via problem instance classification
Rainbow of computer science
Approximation algorithms for scheduling and packing problems
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Scheduling jobs on identical and uniform processors revisited
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Moderately exponential approximation for makespan minimization on related machines
Theoretical Computer Science
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We present an efficient polynomial time approximation scheme (EPTAS) for scheduling on uniform processors, i.e., finding a minimum length schedule for a set of $n$ independent jobs on $m$ processors with different speeds (a fundamental NP-hard scheduling problem). The previous best polynomial time approximation scheme (PTAS) by Hochbaum and Shmoys has a running time of $(n/\epsilon)^{O(1/\epsilon^2)}$. Our algorithm, based on a new mixed integer linear program (MILP) formulation with a constant number of integral variables and an interesting rounding method, finds a schedule whose length is within a relative error $\epsilon$ of the optimum and has a running time of $2^{O(1/\epsilon^2\log(1/\epsilon)^3)}+poly(n)$.